2024/05/31 by Daniel Duffy, Duffy, Daniel, Itay Griniasty +5
Engineering · #Advanced Materials and Mechanics #Architecture and Computational Design #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Modular Robots and Swarm Intelligence #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2405.21024
openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Shape-programmed sheets morph from one surface into another upon activation by stimuli such as illumination, and have attracted much interest for their potential engineering applications, especially in soft robotics. Complex shape changes can be achieved by patterning a simple local active deformation (e.g. isotropic swelling), to generate differential growth. Usually the material itself is designed \unicodex2014 for example by patterning a molecular director \unicodex2014 such that a particular shape change occurs upon exposure to a spatially uniform stimulus. A limitation of this paradigm is that typically only one target geometry can be attained as the stimulus is adjusted. Here we show that this limitation can be overcome by patterning the stimulus itself, thereby exercising spatiotemporal control over local deformation magnitudes. Thus a single physical sample can be induced to traverse a continuous family of target geometries, opening the door to precise shape adjustments, new functionalities, and designable non-reciprocal loops in shape space. We illustrate these possibilities with examples including active parabolic reflectors, chiral flow guides, and bending channels. Finding the necessary patterns of activation involves solving families of metric inverse problems; we solve these by reduction to ODEs in an axisymmetric setting, then present a novel numerical scheme to solve them in generality.